Holdings: Monte Carlo methods in fuzzy optimization

Monte Carlo methods in fuzzy optimization:

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Bibliographic Details
Main Authors:	Buckley, James J. 1936- (Author), Jowers, Leonard J. (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer 2008
Series:	Studies in fuzziness and soft computing 222
Subjects:	Fuzzy systems Monte Carlo method Monte-Carlo-Simulation Fuzzy-Optimierung
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Item Description:	Literaturangaben
Physical Description:	XIII, 260 S. graph. Darst. 24 cm
ISBN:	9783540762898

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adam_text	JAMES J. BUCKLEY AND LEONARD J. JOWERS MONTE CARLO METHODS IN FUZZY OPTIMIZATION CONTENTS PART I: INTRODUCTION 1 INTRODUCTION 3 1.1 INTRODUCTION 3 1.1.1 PARTI 3 1.1.2 PART II 4 1.1.3 PART III 4 1.1.4 PART IV 4 1.2 NOTATION 5 1.3 PREVIOUS RESEARCH 5 1.4 MATLAB/C++ PROGRAMS 6 REFERENCES 6 2 FUZZY SETS 9 2.1 INTRODUCTION 9 2.2 FUZZY SETS .- 9 2.2.1 FUZZY NUMBERS 10 2.2.2 ALPHA-CUTS 11 2.2.3 INEQUALITIES 12 2.2.4 DISCRETE FUZZY SETS 13 2.3 FUZZY ARITHMETIC 13 2.3.1 EXTENSION PRINCIPLE 13 2.3.2 INTERVAL ARITHMETIC 14 2.3.3 FUZZY ARITHMETIC 15 2.4 FUZZY FUNCTIONS 16 2.4.1 EXTENSION PRINCIPLE 16 2.4.2 ALPHA-CUTS AND INTERVAL ARITHMETIC 17 2.4.3 DIFFERENCES 17 2.5 MIN/MAX OF A FUZZY NUMBER 18 2.6 ORDERING FUZZY NUMBERS 20 2.6.1 BUCKLEY S METHOD 20 2.6.2 KERRE S METHOD 21 2.6.3 CHEN S METHOD 22 2.6.4 BREAKING TIES 24 VIII CONTENTS 2.7 UNDOMINATED FUZZY VECTORS 24 2.7.1 BUCKLEY S METHOD 26 2.7.2 KERRE S METHOD 27 2.7.3 CHEN S METHOD 27 REFERENCES 27 3 CRISP RANDOM NUMBERS AND VECTORS 2 9 3.1 INTRODUCTION 29 3.2 RANDOM NUMBERS 29 3.2.1 QUASI-RANDOM SEQUENCES 30 3.2.2 RANDOM NUMBER GENERATOR 31 3.3 RANDOM NON-NEGATIVE INTEGERS 32 3.4 RANDOM VECTORS: REAL NUMBERS 32 3.5 RANDOM VECTORS: NON-NEGATIVE INTEGERS 34 REFERENCES 34 4 RANDOM FUZZY NUMBERS AND VECTORS 35 4.1 INTRODUCTION 35 4.2 RANDOM TRIANGULAR/TRAPEZOIDAL FUZZY NUMBERS 35 4.3 RANDOM QUADRATIC FUZZY NUMBERS 36 4.3.1 GENERATED FROM IMPLICIT QUADRATIC FUNCTIONS 36 4.3.2 GENERATED FROM PARAMETRIC QUADRATIC FUNCTIONS, BEZIER FUZZY NUMBERS 38 4.4 COMPARISON OF RANDOM FUZZY VECTORS 40 4.5 RANDOM FUZZY VECTORS 41 REFERENCES 42 5 TESTS FOR RANDOMNESS 43 5.1 INTRODUCTION 43 5.2 RANDOM FUZZY NUMBERS 43 5.2.1 RUN TEST 43 5.2.2 FREQUENCY TEST 47 5.3 SEARCH SPACE 50 5.3.1 SEARCH SPACE [A, B] FOR QBGFNS 50 5.3.2 SEARCH SPACE Q FOR QBGFNS 52 5.3.3 SEARCH SPACE [A, B] FOR TFNS 52 5.3.4 SEARCH SPACE Q FOR TFNS 52 5.3.5 OTHER SEARCH SPACES 53 REFERENCES 53 PART II: APPLICATIONS 6 FUZZY MONTE CARLO METHOD 57 6.1 INTRODUCTION 57 6.2 CRISP LINEAR PROGRAM 57 6.3 FUZZY LINEAR PROGRAM 58 6.3.1 KERRE S METHOD 59 CONTENTS IX 6.3.2 CHEN S METHOD 61 6.3.3 COMPARISON OF SOLUTIONS 63 REFERENCES 64 7 FULLY FUZZIFIED LINEAR PROGRAMMING 1 67 7.1 INTRODUCTION 67 7.2 FULLY FUZZIFIED LINEAR PROGRAMMING 67 7.3 PRODUCT MIX PROBLEM 68 7.4 FUZZY MONTE CARLO METHOD 69 7.4.1 KERRE S METHOD 69 7.4.2 CHEN S METHOD 71 7.5 COMPARISON OF SOLUTIONS 72 REFERENCES 73 8 FULLY FUZZIFIED LINEAR PROGRAMMING II 75 8.1 INTRODUCTION 75 8.2 DIET PROBLEM 75 8.3 FUZZY MONTE CARLO METHOD 76 8.4 COMPARISON OF SOLUTIONS 78 REFERENCES 80 9 FUZZY MULTIOBJECTIVE LP 81 9.1 INTRODUCTION 81 9.2 MULTIOBJECTIVE FULLY FUZZIFIED LINEAR PROGRAMMING 81 9.3 EXAMPLE PROBLEM 82 9.4 FUZZY MONTE CARLO METHOD 83 9.5 COMPARE SOLUTIONS 86 REFERENCES 87 10 SOLVING FUZZY EQUATIONS 89 10.1 INTRODUCTION 89 10.2 AJ( + B = C 89 10.2.1 OTHER SOLUTIONS 91 10.2.2 FUZZY MONTE CARLO METHOD 94 10.3 FUZZY QUADRATIC EQUATION 98 10.3.1 FUZZY MONTE CARLO METHOD 100 10.4 FUZZY MATRIX EQUATION 103 10.4.1 FUZZY MONTE CARLO METHOD 110 10.5 SUMMARY AND CONCLUSIONS 114 REFERENCES 114 11 FUZZY LINEAR REGRESSION I 11 7 11.1 INTRODUCTION 117 11.2 RANDOM FUZZY VECTORS 118 11.3 APPLICATION 119 11.3.1 FIRST CHOICE OF INTERVALS 119 X CONTENTS 11.3.2 SECOND CHOICE OF INTERVALS 120 11.3.3 COMPARISON OF SOLUTIONS 122 11.4 SUMMARY AND CONCLUSIONS 123 REFERENCES 124 12 UNIVARIATE FUZZY NONLINEAR REGRESSION 127 12.1 INTRODUCTION 127 12.2 UNIVARIATE FUZZY NONLINEAR REGRESSION 128 12.2.1 EVOLUTIONARY ALGORITHM (EA) 129 12.3 FUZZY MONTE CARLO METHOD 129 12.4 FUZZY QUADRATIC 130 12.4.1 FIRST CHOICE OF INTERVALS 130 12.4.2 SECOND CHOICE OF INTERVALS 132 12.4.3 COMPARISON OF SOLUTIONS 133 12.5 FUZZY LOGARITHMIC 133 12.5.1 FIRST CHOICE OF INTERVALS 133 12.5.2 SECOND CHOICE OF INTERVALS 134 12.5.3 COMPARISON OF SOLUTIONS 135 12.6 SUMMARY AND CONCLUSIONS 136 REFERENCES 136 13 MULTIVARIATE NONLINEAR REGRESSION 139 13.1 INTRODUCTION 139 13.2 UNIVERSAL APPROXIMATOR 139 13.3 EVOLUTIONARY ALGORITHM 140 13.4 FUZZY MONTE CARLO METHOD 141 13.5 APPLICATIONS 142 13.5.1 FIRST APPLICATION 7 142 13.5.2 SECOND APPLICATION 145 13.5.3 THIRD APPLICATION 147 13.5.4 FOURTH APPLICATION 149 13.6 SUMMARY AND CONCLUSIONS 153 REFERENCES 154 14 FUZZY LINEAR REGRESSION II 155 14.1 INTRODUCTION 155 14.2 ERROR MEASURES 156 14.3 RANDOM VECTORS 157 14.4 EXAMPLE PROBLEM 157 14.4.1 FIRST CHOICE OF INTERVALS 158 14.4.2 SECOND CHOICE OF INTERVALS 159 14.4.3 COMPARISON OF SOLUTIONS 160 14.5 SUMMARY AND CONCLUSIONS 161 14.6 MATLAB PROGRAM 162 REFERENCES 163 CONTENTS XI 15 FUZZY TWO-PERSON ZERO-SUM GAMES 165 15.1 INTRODUCTION 165 15.2 TWO-PERSON ZERO-SUM GAMES 165 15.3 FUZZY TWO-PERSON ZERO-SUM GAMES 166 15.4 FUZZY MONTE CARLO 169 15.4.1 RANDOM SEQUENCES OF FUZZY MIXED STRATEGIES 170 15.4.2 MAX/MIN OF FUZZY NUMBERS 170 15.4.3 FUZZY MONTE CARLO SOLUTION METHOD 171 15.5 CONCLUSIONS AND FUTURE RESEARCH 172 REFERENCES 173 16 FUZZY QUEUING MODELS 175 16.1 INTRODUCTION 175 16.2 QUEUING MODEL 175 16.3 FUZZY QUEUING MODEL 177 16.4 FUZZY MONTE CARLO METHOD 180 16.4.1 RANDOM SEQUENCE V K 180 16.4.2 MAXIMUM OF FUZZY PROFIT 180 16.5 FUZZY MONTE CARLO SOLUTION 181 16.6 SUMMARY AND CONCLUSIONS 183 REFERENCES 184 PART III: UNFINISHED BUSINESS 17 FUZZY MIN-COST CAPACITATED NETWORK . 187 17.1 INTRODUCTION 187 17.2 MIN-COST CAPACITATED NETWORK 187 17.3 FUZZY MONTE CARLO METHOD 190 REFERENCES 190 18 FUZZY SHORTEST PATH PROBLEM 191 18.1 INTRODUCTION 191 18.2 FUZZY SHORTEST PATH PROBLEM 191 18.3 MONTE CARLO METHOD 192 REFERENCES 193 19 FUZZY MAX-FLOW PROBLEM 195 19.1 INTRODUCTION 195 19.2 MAX-FLOW PROBLEM 195 19.3 FUZZY MAX-FLOW PROBLEM 196 19.3.1 FUZZY MONTE CARLO SOLUTION 197 REFERENCES 198 XII CONTENTS 20 INVENTORY CONTROL: KNOWN DEMAND 199 20.1 INTRODUCTION 199 20.2 INVENTORY PROBLEM 199 20.3 MONTE CARLO METHOD 202 20.3.1 MONTE CARLO SOLUTION 203 REFERENCES 204 21 INVENTORY CONTROL: FUZZY DEMAND 205 21.1 INTRODUCTION 205 21.2 INVENTORY MODEL 205 21.2.1 MONTE CARLO SOLUTION 211 22 INVENTORY CONTROL: BACKORDERING 213 22.1 INTRODUCTION 213 22.2 INVENTORY MODEL 213 22.3 MONTE CARLO METHOD 214 REFERENCES 216 23 FUZZY TRANSPORTATION PROBLEM 217 23.1 INTRODUCTION 217 23.2 TRANSPORTATION PROBLEM 217 23.3 FUZZY TRANSPORTATION PROBLEM 218 REFERENCES 220 24 FUZZY INTEGER PROGRAMMING 223 24.1 INTRODUCTION 223 24.2 FUZZY INTEGERS 223 24.3 AN INTEGER PROGRAMMING PROBLEM 224 24.4 A FUZZY INTEGER PROGRAMMING PROBLEM 224 24.4.1 FUZZY MONTE CARLO SOLUTION 225 REFERENCES 226 25 FUZZY DYNAMIC PROGRAMMING 227 25.1 INTRODUCTION 227 25.2 A DYNAMIC PROGRAMMING PROBLEM 227 25.3 A FUZZY DYNAMIC PROGRAMMING PROBLEM 228 25.3.1 FUZZY MONTE CARLO SOLUTION 229 REFERENCES 229 26 FUZZY PROJECT SCHEDULING/PERT 231 26.1 INTRODUCTION 231 26.2 JOB TIMES FUZZY NUMBERS 232 26.3 JOB TIMES DISCRETE FUZZY SETS 234 26.3.1 FUZZY MONTE CARLO METHOD 234 REFERENCES 235 CONTENTS XIII 27 MAX/MIN FUZZY FUNCTION 237 27.1 INTRODUCTION 237 27.2 MAX/MIN F(X)^ 237 27.3 MAX/MIN F(X, Y) 238 REFERENCES 239 PART IV: SUMMARY, CONCLUSIONS, FUTURE RESEARCH 28 SUMMARY, CONCLUSIONS, FUTURE RESEARCH 243 28.1 SUMMARY 243 28.2 FUTURE RESEARCH 244 28.3 CONCLUSIONS 245 INDEX 247 LIST OF FIGURES 253 LIST OF TABLES 257
adam_txt	JAMES J. BUCKLEY AND LEONARD J. JOWERS MONTE CARLO METHODS IN FUZZY OPTIMIZATION CONTENTS PART I: INTRODUCTION 1 INTRODUCTION 3 1.1 INTRODUCTION 3 1.1.1 PARTI 3 1.1.2 PART II 4 1.1.3 PART III 4 1.1.4 PART IV 4 1.2 NOTATION 5 1.3 PREVIOUS RESEARCH 5 1.4 MATLAB/C++ PROGRAMS 6 REFERENCES 6 2 FUZZY SETS 9 2.1 INTRODUCTION 9 2.2 FUZZY SETS .- 9 2.2.1 FUZZY NUMBERS 10 2.2.2 ALPHA-CUTS 11 2.2.3 INEQUALITIES 12 2.2.4 DISCRETE FUZZY SETS 13 2.3 FUZZY ARITHMETIC 13 2.3.1 EXTENSION PRINCIPLE 13 2.3.2 INTERVAL ARITHMETIC 14 2.3.3 FUZZY ARITHMETIC 15 2.4 FUZZY FUNCTIONS 16 2.4.1 EXTENSION PRINCIPLE 16 2.4.2 ALPHA-CUTS AND INTERVAL ARITHMETIC 17 2.4.3 DIFFERENCES 17 2.5 MIN/MAX OF A FUZZY NUMBER 18 2.6 ORDERING FUZZY NUMBERS 20 2.6.1 BUCKLEY'S METHOD 20 2.6.2 KERRE'S METHOD 21 2.6.3 CHEN'S METHOD 22 2.6.4 BREAKING TIES 24 VIII CONTENTS 2.7 UNDOMINATED FUZZY VECTORS 24 2.7.1 BUCKLEY'S METHOD 26 2.7.2 KERRE'S METHOD 27 2.7.3 CHEN'S METHOD 27 REFERENCES 27 3 CRISP RANDOM NUMBERS AND VECTORS 2 9 3.1 INTRODUCTION 29 3.2 RANDOM NUMBERS 29 3.2.1 QUASI-RANDOM SEQUENCES 30 3.2.2 RANDOM NUMBER GENERATOR 31 3.3 RANDOM NON-NEGATIVE INTEGERS 32 3.4 RANDOM VECTORS: REAL NUMBERS 32 3.5 RANDOM VECTORS: NON-NEGATIVE INTEGERS 34 REFERENCES 34 4 RANDOM FUZZY NUMBERS AND VECTORS 35 4.1 INTRODUCTION 35 4.2 RANDOM TRIANGULAR/TRAPEZOIDAL FUZZY NUMBERS 35 4.3 RANDOM QUADRATIC FUZZY NUMBERS 36 4.3.1 GENERATED FROM IMPLICIT QUADRATIC FUNCTIONS 36 4.3.2 GENERATED FROM PARAMETRIC QUADRATIC FUNCTIONS, BEZIER FUZZY NUMBERS 38 4.4 COMPARISON OF RANDOM FUZZY VECTORS 40 4.5 RANDOM FUZZY VECTORS 41 REFERENCES 42 5 TESTS FOR RANDOMNESS 43 5.1 INTRODUCTION 43 5.2 RANDOM FUZZY NUMBERS 43 5.2.1 RUN TEST 43 5.2.2 FREQUENCY TEST 47 5.3 SEARCH SPACE 50 5.3.1 SEARCH SPACE [A, B] FOR QBGFNS 50 5.3.2 SEARCH SPACE Q FOR QBGFNS 52 5.3.3 SEARCH SPACE [A, B] FOR TFNS 52 5.3.4 SEARCH SPACE Q FOR TFNS 52 5.3.5 OTHER SEARCH SPACES 53 REFERENCES 53 PART II: APPLICATIONS 6 FUZZY MONTE CARLO METHOD 57 6.1 INTRODUCTION 57 6.2 CRISP LINEAR PROGRAM 57 6.3 FUZZY LINEAR PROGRAM 58 6.3.1 KERRE'S METHOD 59 CONTENTS IX 6.3.2 CHEN'S METHOD 61 6.3.3 COMPARISON OF SOLUTIONS 63 REFERENCES 64 7 FULLY FUZZIFIED LINEAR PROGRAMMING 1 67 7.1 INTRODUCTION 67 7.2 FULLY FUZZIFIED LINEAR PROGRAMMING 67 7.3 PRODUCT MIX PROBLEM 68 7.4 FUZZY MONTE CARLO METHOD 69 7.4.1 KERRE'S METHOD 69 7.4.2 CHEN'S METHOD 71 7.5 COMPARISON OF SOLUTIONS 72 REFERENCES 73 8 FULLY FUZZIFIED LINEAR PROGRAMMING II 75 8.1 INTRODUCTION 75 8.2 DIET PROBLEM 75 8.3 FUZZY MONTE CARLO METHOD 76 8.4 COMPARISON OF SOLUTIONS 78 REFERENCES 80 9 FUZZY MULTIOBJECTIVE LP 81 9.1 INTRODUCTION 81 9.2 MULTIOBJECTIVE FULLY FUZZIFIED LINEAR PROGRAMMING 81 9.3 EXAMPLE PROBLEM 82 9.4 FUZZY MONTE CARLO METHOD 83 9.5 COMPARE SOLUTIONS 86 REFERENCES 87 10 SOLVING FUZZY EQUATIONS 89 10.1 INTRODUCTION 89 10.2 AJ( + B = C 89 10.2.1 OTHER SOLUTIONS 91 10.2.2 FUZZY MONTE CARLO METHOD 94 10.3 FUZZY QUADRATIC EQUATION 98 10.3.1 FUZZY MONTE CARLO METHOD 100 10.4 FUZZY MATRIX EQUATION 103 10.4.1 FUZZY MONTE CARLO METHOD 110 10.5 SUMMARY AND CONCLUSIONS 114 REFERENCES 114 11 FUZZY LINEAR REGRESSION I 11 7 11.1 INTRODUCTION 117 11.2 RANDOM FUZZY VECTORS 118 11.3 APPLICATION 119 11.3.1 FIRST CHOICE OF INTERVALS 119 X CONTENTS 11.3.2 SECOND CHOICE OF INTERVALS 120 11.3.3 COMPARISON OF SOLUTIONS 122 11.4 SUMMARY AND CONCLUSIONS 123 REFERENCES 124 12 UNIVARIATE FUZZY NONLINEAR REGRESSION 127 12.1 INTRODUCTION 127 12.2 UNIVARIATE FUZZY NONLINEAR REGRESSION 128 12.2.1 EVOLUTIONARY ALGORITHM (EA) 129 12.3 FUZZY MONTE CARLO METHOD 129 12.4 FUZZY QUADRATIC 130 12.4.1 FIRST CHOICE OF INTERVALS 130 12.4.2 SECOND CHOICE OF INTERVALS 132 12.4.3 COMPARISON OF SOLUTIONS 133 12.5 FUZZY LOGARITHMIC 133 12.5.1 FIRST CHOICE OF INTERVALS 133 12.5.2 SECOND CHOICE OF INTERVALS 134 12.5.3 COMPARISON OF SOLUTIONS 135 12.6 SUMMARY AND CONCLUSIONS 136 REFERENCES 136 13 MULTIVARIATE NONLINEAR REGRESSION 139 13.1 INTRODUCTION 139 13.2 UNIVERSAL APPROXIMATOR 139 13.3 EVOLUTIONARY ALGORITHM 140 13.4 FUZZY MONTE CARLO METHOD 141 13.5 APPLICATIONS 142 13.5.1 FIRST APPLICATION 7 142 13.5.2 SECOND APPLICATION 145 13.5.3 THIRD APPLICATION 147 13.5.4 FOURTH APPLICATION 149 13.6 SUMMARY AND CONCLUSIONS 153 REFERENCES 154 14 FUZZY LINEAR REGRESSION II 155 14.1 INTRODUCTION 155 14.2 ERROR MEASURES 156 14.3 RANDOM VECTORS 157 14.4 EXAMPLE PROBLEM 157 14.4.1 FIRST CHOICE OF INTERVALS 158 14.4.2 SECOND CHOICE OF INTERVALS 159 14.4.3 COMPARISON OF SOLUTIONS 160 14.5 SUMMARY AND CONCLUSIONS 161 14.6 MATLAB PROGRAM 162 REFERENCES 163 CONTENTS XI 15 FUZZY TWO-PERSON ZERO-SUM GAMES 165 15.1 INTRODUCTION 165 15.2 TWO-PERSON ZERO-SUM GAMES 165 15.3 FUZZY TWO-PERSON ZERO-SUM GAMES 166 15.4 FUZZY MONTE CARLO 169 15.4.1 RANDOM SEQUENCES OF FUZZY MIXED STRATEGIES 170 15.4.2 MAX/MIN OF FUZZY NUMBERS 170 15.4.3 FUZZY MONTE CARLO SOLUTION METHOD 171 15.5 CONCLUSIONS AND FUTURE RESEARCH 172 REFERENCES 173 16 FUZZY QUEUING MODELS 175 16.1 INTRODUCTION 175 16.2 QUEUING MODEL 175 16.3 FUZZY QUEUING MODEL 177 16.4 FUZZY MONTE CARLO METHOD 180 16.4.1 RANDOM SEQUENCE V K 180 16.4.2 MAXIMUM OF FUZZY PROFIT 180 16.5 FUZZY MONTE CARLO SOLUTION 181 16.6 SUMMARY AND CONCLUSIONS 183 REFERENCES 184 PART III: UNFINISHED BUSINESS 17 FUZZY MIN-COST CAPACITATED NETWORK . 187 17.1 INTRODUCTION 187 17.2 MIN-COST CAPACITATED NETWORK 187 17.3 FUZZY MONTE CARLO METHOD 190 REFERENCES 190 18 FUZZY SHORTEST PATH PROBLEM 191 18.1 INTRODUCTION 191 18.2 FUZZY SHORTEST PATH PROBLEM 191 18.3 MONTE CARLO METHOD 192 REFERENCES 193 19 FUZZY MAX-FLOW PROBLEM 195 19.1 INTRODUCTION 195 19.2 MAX-FLOW PROBLEM 195 19.3 FUZZY MAX-FLOW PROBLEM 196 19.3.1 FUZZY MONTE CARLO SOLUTION 197 REFERENCES 198 XII CONTENTS 20 INVENTORY CONTROL: KNOWN DEMAND 199 20.1 INTRODUCTION 199 20.2 INVENTORY PROBLEM 199 20.3 MONTE CARLO METHOD 202 20.3.1 MONTE CARLO SOLUTION 203 REFERENCES 204 21 INVENTORY CONTROL: FUZZY DEMAND 205 21.1 INTRODUCTION 205 21.2 INVENTORY MODEL 205 21.2.1 MONTE CARLO SOLUTION 211 22 INVENTORY CONTROL: BACKORDERING 213 22.1 INTRODUCTION 213 22.2 INVENTORY MODEL 213 22.3 MONTE CARLO METHOD 214 REFERENCES 216 23 FUZZY TRANSPORTATION PROBLEM 217 23.1 INTRODUCTION 217 23.2 TRANSPORTATION PROBLEM 217 23.3 FUZZY TRANSPORTATION PROBLEM 218 REFERENCES 220 24 FUZZY INTEGER PROGRAMMING 223 24.1 INTRODUCTION 223 24.2 FUZZY INTEGERS 223 24.3 AN INTEGER PROGRAMMING PROBLEM 224 24.4 A FUZZY INTEGER PROGRAMMING PROBLEM 224 24.4.1 FUZZY MONTE CARLO SOLUTION 225 REFERENCES 226 25 FUZZY DYNAMIC PROGRAMMING 227 25.1 INTRODUCTION 227 25.2 A DYNAMIC PROGRAMMING PROBLEM 227 25.3 A FUZZY DYNAMIC PROGRAMMING PROBLEM 228 25.3.1 FUZZY MONTE CARLO SOLUTION 229 REFERENCES 229 26 FUZZY PROJECT SCHEDULING/PERT 231 26.1 INTRODUCTION 231 26.2 JOB TIMES FUZZY NUMBERS 232 26.3 JOB TIMES DISCRETE FUZZY SETS 234 26.3.1 FUZZY MONTE CARLO METHOD 234 REFERENCES 235 CONTENTS XIII 27 MAX/MIN FUZZY FUNCTION 237 27.1 INTRODUCTION 237 27.2 MAX/MIN F(X)^ 237 27.3 MAX/MIN F(X, Y) 238 REFERENCES 239 PART IV: SUMMARY, CONCLUSIONS, FUTURE RESEARCH 28 SUMMARY, CONCLUSIONS, FUTURE RESEARCH 243 28.1 SUMMARY 243 28.2 FUTURE RESEARCH 244 28.3 CONCLUSIONS 245 INDEX 247 LIST OF FIGURES 253 LIST OF TABLES 257
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id	DE-604.BV035054911
illustrated	Illustrated
index_date	2024-07-02T21:58:06Z
indexdate	2024-07-09T21:21:10Z
institution	BVB
isbn	9783540762898
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016723513
oclc_num	214304413
open_access_boolean
owner	DE-703 DE-824 DE-355 DE-BY-UBR
owner_facet	DE-703 DE-824 DE-355 DE-BY-UBR
physical	XIII, 260 S. graph. Darst. 24 cm
publishDate	2008
publishDateSearch	2008
publishDateSort	2008
publisher	Springer
record_format	marc
series	Studies in fuzziness and soft computing
series2	Studies in fuzziness and soft computing
spelling	Buckley, James J. 1936- Verfasser (DE-588)120637871 aut Monte Carlo methods in fuzzy optimization James J. Buckley and Leonard J. Jowers Berlin ; Heidelberg Springer 2008 XIII, 260 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Studies in fuzziness and soft computing 222 Literaturangaben Fuzzy systems Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Fuzzy-Optimierung (DE-588)4659945-9 gnd rswk-swf Fuzzy-Optimierung (DE-588)4659945-9 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Jowers, Leonard J. Verfasser aut Erscheint auch als Online-Ausgabe 978-3-540-76290-4 Studies in fuzziness and soft computing 222 (DE-604)BV021858135 222 http://d-nb.info/985771089/04 Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016723513&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Buckley, James J. 1936- Jowers, Leonard J. Monte Carlo methods in fuzzy optimization Studies in fuzziness and soft computing Fuzzy systems Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Fuzzy-Optimierung (DE-588)4659945-9 gnd
subject_GND	(DE-588)4240945-7 (DE-588)4659945-9
title	Monte Carlo methods in fuzzy optimization
title_auth	Monte Carlo methods in fuzzy optimization
title_exact_search	Monte Carlo methods in fuzzy optimization
title_exact_search_txtP	Monte Carlo methods in fuzzy optimization
title_full	Monte Carlo methods in fuzzy optimization James J. Buckley and Leonard J. Jowers
title_fullStr	Monte Carlo methods in fuzzy optimization James J. Buckley and Leonard J. Jowers
title_full_unstemmed	Monte Carlo methods in fuzzy optimization James J. Buckley and Leonard J. Jowers
title_short	Monte Carlo methods in fuzzy optimization
title_sort	monte carlo methods in fuzzy optimization
topic	Fuzzy systems Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Fuzzy-Optimierung (DE-588)4659945-9 gnd
topic_facet	Fuzzy systems Monte Carlo method Monte-Carlo-Simulation Fuzzy-Optimierung
url	http://d-nb.info/985771089/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016723513&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV021858135
work_keys_str_mv	AT buckleyjamesj montecarlomethodsinfuzzyoptimization AT jowersleonardj montecarlomethodsinfuzzyoptimization

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